Synchronization of linear oscillators coupled through a dynamic network with interior nodes

TUNA S. E.

AUTOMATICA, vol.117, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 117
  • Publication Date: 2020
  • Doi Number: 10.1016/j.automatica.2020.109008
  • Journal Name: AUTOMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Applied Science & Technology Source, Aqualine, Communication Abstracts, Compendex, Computer & Applied Sciences, Information Science and Technology Abstracts, INSPEC, MathSciNet, zbMATH, DIALNET, Library, Information Science & Technology Abstracts (LISTA)
  • Keywords: Synchronization, Schur complement, Linear oscillator, Interior node, HARMONIC-OSCILLATORS, ELECTRICAL NETWORKS, MULTIAGENT SYSTEMS, KRON REDUCTION
  • Middle East Technical University Affiliated: Yes

Abstract

Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network is allowed to contain interior nodes, i.e., those that are not directly connected to an oscillator. It is shown that the oscillators asymptotically synchronize if and only if the Schur complement (with respect to the boundary nodes) of the complex-valued Laplacian matrix representing the coupling has a single eigenvalue on the imaginary axis. (C) 2020 Elsevier Ltd. All rights reserved.